Akadémiai Kiadó

The fundamental concepts dealt with here are the structure of parentheses and the ρ-multiplications of vectors, in the latter case the product of two vectors is again a vector and the structure (for a given ρ) is a semigroup. By means of a multiplicative structure it is possible to introduce the concept of the coded structure and a procedure for solving coding and decoding problems can then be given. In addition, applications for rings and finite algebras are illustrated. To demonstrate other applications, a process is given for approximating an arbitrary distribution vector starting from uniform distribution, a novel theorem is given for the theory of games. An extremely useful feature of the structure of vectorproducts is that it can easily be implemented on a computer.